Senior Republican figures attempted to downplay the role of money in the presidential race Sunday, as Barack Obama embarked on a new push for funds having already announced a record monthly haul.

Speaking on CNN's State of the Union, Republican national committee chairman Reince Priebus prompted speculation that Democrats were opening up a war-chest gap as the election heads into its final month.

A day after Obama announced a $181m total for September donations – the highest monthly total posted by either candidate to date – Priebus admitted that he was unsure that Republican candidate Mitt Romney would be able to match what he described as as an "impressive number".

"We all understand that this race isn't going to come down to money," he added, while suggesting that the Republicans still had "all the money we need to be competitive".

Obama's announcement, made via a tweet Saturday, that supporters had helped amass the largest one-month fundraising total for his re-election campaign has taken the wind out of the Republican sails following what was widely seen as a win for Romney in the first presidential debate on Wednesday night.

That victory appears to have been short-lived. A little more than 24 hours after the inaugural head-to-head, new job figures came out that gave cheer to Obama's re-election efforts.

Friday's monthly unemployment data revealed that the US had added 114,000 new jobs in September, in line with expectation.

But a dramatic upwards revision of the previous month's data, from 96,000 to 142,000 new jobs, saw the headline unemployment rate fall to 7.8%, from 8.1% – the first dip below 8% since Obama took office in January 2009.

It enabled the president to shrug off the disappointment of a lacklustre debate performance.

The job figures were "a reminder that this country has come too far to turn back now", he told supporters while on the stump in Virginia.

Romney countered that "by any rational measure, it is crystal clear we are in the middle of a jobs crisis".

But the news is likely to eat into any debate bump the Republican candidate may have been expecting.

As it is, polls suggest that a strong performance during the head-to-head exchange on Wednesday – broadcast to an estimated audience of 67 million viewers – has not done enough to tip the balance in Romney's favour.

An Ipsos/Reuters snapshot of voter intention released Saturday evening found that Obama maintained an advantage, albeit a reduced one.

The survey, conducted after the debate was aired, put the Democrat ahead by two points, with a 47% to 45% lead over Romney.

It is down from the six point margin he had held in some polls prior to Wednesday. But it nonetheless indicates that the Republican challenger still has some way to go in convincing swing voters.

Ipsos pollster Julia Clark said: "We haven't seen additional gains from Romney. This suggests to me that this is more of a bounce than a permanent shift."

The task of turning around the polls could be made harder for the Republican challenger if his campaign finances for September show a shortfall in donations when compared to the White House incumbent.

Figures from the Federal Election Commission revealed that in August, Obama pulled ahead in terms of monthly donations, with $114m compared to $111m for Romney.

Meanwhile, greater spending earlier in the race has depleted the Republican candidate's war chest, undermining claims that he had a cash advantage over his rival.

Priebus, on CNN's State of the Union, said the impressive fundraising figures of Obama were "no surprise", adding: "I've been saying that President Obama is going to raise a billion dollars for a year and a half".

But behind the scenes, Romney backers may be getting jittery over the greater spend potential of the Obama camp. The additional cash is likely to pay dividends when it comes to attack ads being played in key battleground states.

In a bid to lock in the cash advantage, Obama embarked on a two-day fundraising push in California on Sunday.

Star-studded bashes are planned in Los Angeles and San Francisco in an effort to milk the lucrative Hollywood and tech industries, thought to bend towards the Democrats.

"There is exactly one month left to go until election day," Obama campaign manager Jim Messina said in an email pitch ahead of the visit.

"The stakes are too high for us to take our foot off the gas now," he added.